• Journal of Semiconductors
  • Vol. 41, Issue 11, 112402 (2020)
Lin Cheng1, Kui Tang1, Wang-Hung Ki2, and Feng Su3
Author Affiliations
  • 1University of Science and Technology of China, Hefei 230024, China
  • 2Hong Kong University of Science and Technology, Hong Kong, China
  • 3Broadcom Limited, San Jose, US
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    DOI: 10.1088/1674-4926/41/11/112402 Cite this Article
    Lin Cheng, Kui Tang, Wang-Hung Ki, Feng Su. Fast-transient techniques for high-frequency DC–DC converters[J]. Journal of Semiconductors, 2020, 41(11): 112402 Copy Citation Text show less

    Abstract

    A 30 MHz voltage-mode controlled buck converter with fast transient responses is presented. An improved differential difference amplifier (DDA)-based Type-III compensator is proposed to reduce the settling times of the converter during load transients, and to achieve near-optimal transient responses with simple PWM control only. Moreover, a hybrid scheme using a digital linear regulator with automatic transient detection and seamless loop transition is proposed to further improve the transient responses. By monitoring the output voltage of the compensator instead of the output voltage of the converter, the proposed hybrid scheme can reduce undershoot and overshoot effectively with good noise immunity and without interrupting the PWM loop. The converter was fabricated in a 0.13 µm standard CMOS process using 3.3 V devices. With an input voltage of 3.3 V, the measured peak efficiencies at the output voltages of 2.4, 1.8, and 1.2 V are 90.7%, 88%, and 83.6%, respectively. With a load step of 1.25 A and rise and fall times of 2 ns, the measured 1% settling times were 220 and 230 ns, with undershoot and overshoot with PWM control of 72 and 76 mV, respectively. They were further reduced to 36 and 38 mV by using the proposed hybrid scheme, and 1% settling times were also reduced to 125 ns.
    $ {V}_{1+}-{V}_{1-}=-\left({V}_{2+}-{V}_{2-}\right) . $ (1)

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    $ {z}_{\mathrm{a}}\left(s\right)=\frac{1}{s{C}_{1}}+{R}_{1}\left|\right|\frac{1}{s{C}_{2}}=\frac{1+s{R}_{1}({C}_{1}+{C}_{2})}{s{C}_{1}(1+s{R}_{1}{C}_{2})}, $ (2)

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    $ {z}_{\mathrm{b}}\left(s\right)={r}_{\mathrm{o}}\left|\right|\frac{1}{s{C}_{\mathrm{m}\mathrm{o}\mathrm{s}}}=\frac{{r}_{\mathrm{o}}}{1+s{C}_{\mathrm{m}\mathrm{o}\mathrm{s}}{r}_{\mathrm{o}}}, $ (3)

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    $ \frac{{V}_{\mathrm{e}\mathrm{a}}-{V}_{\mathrm{G}\mathrm{m}}}{{z}_{\mathrm{a}}\left(s\right)}+{G}_{\mathrm{m}}\left({V}_{\mathrm{e}\mathrm{a}}-{V}_{\mathrm{G}\mathrm{m}}\right)=\frac{{V}_{\mathrm{G}\mathrm{m}}}{{z}_{\mathrm{b}}\left(s\right)}, $ (4)

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    $ \frac{{V}_{\mathrm{G}\mathrm{m}}}{{V}_{\mathrm{e}\mathrm{a}}}=\frac{\left[1+{G}_{\mathrm{m}}{z}_{\mathrm{a}}\left(s\right)\right]{z}_{\mathrm{b}}\left(s\right)}{\left[1+{G}_{\mathrm{m}}{z}_{\mathrm{a}}\left(s\right)\right]{z}_{\mathrm{b}}\left(s\right)+{z}_{\mathrm{a}}\left(s\right)}. $ (5)

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    $ \left({V}_{1+}-{V}_{1-}\right)s{C}_{1}=\frac{{V}_{1-}-{V}_{\mathrm{e}\mathrm{a}}}{{R}_{1}\left|\right|\dfrac{1}{s{C}_{2}}} . $ (6)

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    $ \frac{{V}_{1-}-{V}_{1+}}{{V}_{\mathrm{e}\mathrm{a}}}=\frac{1+s{R}_{1}{C}_{2}}{1+s{R}_{1}\left({C}_{1}+{C}_{2}\right)}\left(1-\frac{{V}_{\mathrm{G}\mathrm{m}}}{{V}_{\mathrm{e}\mathrm{a}}}\right). $ (7)

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    $ A\left(s\right)=-\frac{{V}_{\mathrm{e}\mathrm{a}}}{{V}_{\mathrm{f}\mathrm{b}}}=\frac{{V}_{\mathrm{e}\mathrm{a}}}{{V}_{2+}-{V}_{2-}}. $ (8)

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    $ A\left(s\right){=G}_{\mathrm{m}}{r}_{\mathrm{o}}\frac{\left(1+s{C}_{\mathrm{m}\mathrm{o}\mathrm{s}}/{G}_{\mathrm{m}}\right)\left[1+s\left({C}_{1}+{C}_{2}\right){R}_{1}\right]}{(1+s{C}_{\mathrm{m}\mathrm{o}\mathrm{s}}{r}_{\mathrm{o}})(1+s{C}_{2}{R}_{1})}+\frac{1+s{C}_{1}{r}_{\mathrm{o}}}{1+s{C}_{\mathrm{m}\mathrm{o}\mathrm{s}}{r}_{\mathrm{o}}}, $ (9)

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    $ A\left(s\right){={G}}_{\mathrm{m}}{r}_{\mathrm{o}}\frac{\left(1+\dfrac{s}{{z}_{1}}\right)\left(1+\dfrac{s}{{z}_{2}}\right)}{\left(1+\dfrac{s}{{p}_{1}}\right)\left(1+\dfrac{s}{{p}_{2}}\right)}, $ (10)

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    $ {p}_{1}=\frac{1}{{C}_{\mathrm{m}\mathrm{o}\mathrm{s}}{r}_{\mathrm{o}}},\quad {p}_{2}=\frac{1}{{C}_{2}{R}_{1}}, $ (11)

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    $ \begin{array}{l} {z}_{1}\!=\!\dfrac{2}{{C}_{1}{R}_{1}\!+\!\dfrac{{C}_{\rm{m}\rm{o}\rm{s}}\!+\!{C}_{1}}{{G}_{\rm{m}}}\!+\!\sqrt{\!\!\left(\!{C}_{1}^{2}{R}_{1}^{2}\!+\!2\dfrac{{{C}_{1}^{2}{R}_{1}-C}_{\rm{m}\rm{o}\rm{s}}{C}_{1}{R}_{1}}{{G}_{\rm{m}}}\!+\!\dfrac{{(C}_{\rm{m}\rm{o}\rm{s}}\!+\!{C}_{1}{)}^{2}}{{G}_{\rm{m}}^{2}} \! \right)}}, \\ {z}_{2}\!=\!\dfrac{2}{{C}_{1}{R}_{1}\!+\!\dfrac{{C}_{\rm{mos}}\!+\!{C}_{1}}{{G}_{\rm{m}}}\!-\!\sqrt{\!\!\left(\!{C}_{1}^{2}{R}_{1}^{2}\!+\!2\dfrac{{{C}_{1}^{2}{R}_{1}-C}_{\rm{m}\rm{o}\rm{s}}{C}_{1}{R}_{1}}{{G}_{\rm{m}}}\!+\!\dfrac{{(\!C}_{\rm{m}\rm{o}\rm{s}}\!+\!{C}_{1}{\!)}^{2}}{{G}_{\rm{m}}^{2}}\!\right)}} . \end{array} $ (12)

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    $ \frac{{V}_{\mathrm{G}\mathrm{m}}}{{V}_{\mathrm{f}\mathrm{b}}}={G}_{\mathrm{m}}{r}_{\mathrm{o}}\frac{1+s{C}_{1}({R}_{1}+1/{G}_{\mathrm{m}})}{\left(1+s{C}_{\mathrm{m}\mathrm{o}\mathrm{s}}{r}_{\mathrm{o}}\right)\left(1+s{C}_{2}{R}_{1}\right)}. $ (13)

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    Lin Cheng, Kui Tang, Wang-Hung Ki, Feng Su. Fast-transient techniques for high-frequency DC–DC converters[J]. Journal of Semiconductors, 2020, 41(11): 112402
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